Magnetometry
Obviously, magnetic measurements (magnetization and magnetic susceptibility) are key to the study of quantum magnetism. The technical challenge is to measure these quantities in small samples, at very low temperatures and in high magnetic fields. Commercial instruments only take us part of the way; the most interesting devices we build ourselves, often as student projects. We use several methods.
For measurements down to 1.8 K and up to 14 T we use a vibrating sample magnetometer (VSM) or an AC susceptometer, which are commercial inserts for our three Quantum Design PPMS systems.
Temperature dependence of the magnetization measured in Pb2VO(PO4)2 using a commercial VSM helps reconstruct the phase diagram of this frustrated ferro-antiferromagnet. For more details see F. Landolt, S. Bettler, Z. Yan, S. Gvasaliya, A. Zheludev, S. Mishra, I. Sheikin, S. Krämer, M. Horvatić, A. Gazizulina, O. Prokhnenko, Pre-saturation phase in the frustrated ferro-antiferromagnet Pb2VO(PO4)2 , Phys. Rev. B 102, 094414 (2020); arXiv:2006.04592.
Very precise magnetization measurements can be done in fields up to 7 T with a SQUID magnetometer, which is also a commercial Quantum Design MPMS system. With a 3He insert we can reach temperatures down to 500 mK. The MPMS can also be used with a customized 6 kbar pressure cell.
Scaling of the critical magnetization near the saturation field in the spin-nematic candidate material BaCdVO(PO4)2. (a) Raw data, taken in the interval 0.5–4 K with our MPMS SQUID magnetometer. (b) Scaling plot revealing a spectacular data collapse. For more details see K. Yu. Povarov, V. K. Bhartiya, Z. Yan, A. Zheludev, Thermodynamics of a frustrated quantum magnet on a square lattice , Phys. Rev. B 99, 024413 (2019); arXiv:1807.09549.
There is no reliable commercial equipment to explore lower temperatures, so we have designed our own. In particular, we have built a differential Faraday force magnetometer (see photo at top of page) that can be used at temperatures as low as 50 mK in fields up to 14 T. The whole device fits in the palm of a hand and resolves magnetic moments of a few 10−9 A m2. It is described in D. Blosser, L. Facheris, A. Zheludev, Miniature capacitive Faraday force magnetometer for magnetization measurements at low temperatures and high magnetic fields , Review of Scientific Instruments 91, 073905 (2020); arXiv:2002.10168.
Magnetization curves of the frustrated 2D antiferromagnet Cs2CoBr4 measured with our Faraday balance magnetometer at 100 mK, revealing a whole cascade of fractional magnetization plateaus. For further details see K. Yu. Povarov, L. Facheris, S. Velja, D. Blosser, Z. Yan, S. Gvasaliya, A. Zheludev, Magnetization plateaux cascade in the frustrated quantum antiferromagnet Cs2CoBr4 , Phys. Rev. Research 2, 043384 (2020); arXiv:2004.09893.
Another tool that we have developed is a magnetic torque meter: it measures the torque the sample experiences in an external magnetic field. The results are difficult to interpret quantitatively, but any "feature" in the torque curves usually indicates a phase transition. This technique is extremely sensitive and allows us to explore the complex phase diagrams of quantum magnets.
Magnetic torque measurements reveal a cascade of quantum phase transitions in the frustrated ferro-antiferromagnet Cs2Cu2Mo3O12. A detailed report can be found in D. Flavián, S. Hayashida, L. Huberich, D. Blosser, K. Yu. Povarov, Z. Yan, S. Gvasaliya, A. Zheludev, Magnetic phase diagram of the linear quantum ferro-antiferromagnet Cs2Cu2Mo3O12 , Phys. Rev. B 101, 224408 (2020); arXiv:2004.10636.
As a rule, magnetic properties of quantum magnets are anisotropic. Their magnetic phase diagrams are, as a result, highly dependent on the field direction. Re-mounting the sample in multiple orientations is very impractical because of the time needed to cool down the sample in the cryostat, measure, warm it up and re-mount. Instead, we have developed a piezoelectric step-motor to rotate the sample mounted on a magnetic torque meter in situ. The device works at dilution-cryostat temperatures.
In this example we employ this device to map out the three-dimensional magnetic phase diagram of the frustrated ferro-antiferromagnetic spin chain compound PbCuSO4(OH)2. For more details see Y. Feng, K. Yu. Povarov, A. Zheludev, Three dimensional magnetic phase diagram of the strongly frustrated quantum spin chain system PbCuSO4(OH)2 , Phys. Rev. B 98, 054419 (2018); arXiv:1804.02215.
Sometimes the magnetic fields we need are too strong to produce in our lab. In these cases we take our samples to one of the high-field user facilities, such as those of the European Magnetic Field Laboratory. We regularly perform experiments using resistive, superconducting and pulsed magnets in Dresden, Toulouse and Grenoble. For a student, these trips are an experience of their own: the biggest pulsed magnets deliver their field in a fraction of a second, with a bang to match.
Evolution of the magnetic Bose-Einstein condensate in (C4H12N2)Cu2(Cl1−xBrx)6 with Br concentration in fields up to 45 T. The false-color plot is of magnetic susceptibility. The data were taken at the pulsed-field facility in Toulouse, France. More details in D. Hüvonen, G. Ballon, A. Zheludev, Field-concentration phase diagram of a quantum spin liquid with bond defects , Phys. Rev. B 88, 094402 (2013); arXiv:1307.2750.